Linear Co-ord Geometry

[iNerd]

Use co-ordinate geometry to show that the line joining the two sides of a triangle is parallel to the third and is half the length of the third.

I can't figure it out - a diagram would be extremely helpful! Thanks

[kamil9876]

Doesn't make sense, unless you mean joining the midpoints of the two sides?

[iNerd]

Doesn't make sense, unless you mean joining the midpoints of the two sides?

Must be...I have no idea...I just wrote the question.

[kamil9876]

Well must be a typo because it should really be "midpoint" of the two sides (then the statement is true). The way the question is stated doesn't specify a single line and in fact we can pick a pair of points one on each side such that the statement is false.

[iNerd]

Well must be a typo because it should really be "midpoint" of the two sides (then the statement is true). The way the question is stated doesn't specify a single line and in fact we can pick a pair of points one on each side such that the statement is false.

Handwritten from tutor -.-

If it is whatever your saying (make the question true) how do you do it?

[luffy]

Well must be a typo because it should really be "midpoint" of the two sides (then the statement is true). The way the question is stated doesn't specify a single line and in fact we can pick a pair of points one on each side such that the statement is false.

True, but even if the question did make sense, it doesn't sound like something in the methods study design? (I hope I have read the study design properly). The way that most people would approach this question, would be the use of vectors, which is part of specialist maths, not Methods (CAS).

[Martoman]

.....lol?

If its the midpoint, its already half the length of the third.

To prove its parallel, draw a picture. Seriously. Intuition dictates that you can't project the line anywhere but on the third line joining the other two sides of the triangle if you wish it to form a closed polygon. lol. soooo its parallel to it.

[kamil9876]

I agree but it is possible with methods but pretty long and ugly:

let the three points of the triangle be . Let by the midpoint of , then we have , likewise if is the midpoint of then we have . Now the next step is to show that is parralel to , to do this we must show that they have the same gradient (or both undefined!). The length part is easy, just use the distance between two points formula.

Enjoy the ugly algebraic work.

[luken93]

yeah this surely isn't a methods question, are you sure he didn't make this question for GMA ATAR?

[iNerd]

yeah this surely isn't a methods question, are you sure he didn't make this question for GMA ATAR?

Linear co-ord geometry falls under Chapter 1 Methods. I dislike the question anyway.

[Martoman]

What kamil is saying is very plausible but they would have to lead you along the question hand in hand walking into the sunset to ask it.

[iNerd]

What kamil is saying is very plausible but they would have to lead you along the question hand in hand walking into the sunset to ask it.

You mean like part a), b) and hence c)? Something like that?

[luffy]

What kamil is saying is very plausible but they would have to lead you along the question hand in hand walking into the sunset to ask it.

You mean like part a), b) and hence c)? Something like that?

Actually, I would like to disagree with my previous post, definitely could come up in methods. Clearly, I haven't done Methods in too long xD.

By the way, if you have done a Kilbaha exam, you would see that they do not need to give a part a), b) and c). Then again, some people think Kilbaha takes things too far. LOL. Also, the parts might make the question somewhat trivial.

[Martoman]

What kamil is saying is very plausible but they would have to lead you along the question hand in hand walking into the sunset to ask it.

You mean like part a), b) and hence c)? Something like that?

Actually, I would like to disagree with my previous post, definitely could come up in methods. Clearly, I haven't done Methods in too long xD.

By the way, if you have done a Kilbaha exam, you would see that they do not need to give a part a), b) and c). Then again, some people think Kilbaha takes things too far. LOL. Also, the parts might make the question somewhat trivial.

vcaa exams case and point.